Dorau–Much projection path

Can pre-geometric recoverability already know about the modular relative entropy that recovers semiclassical Einstein equations?

Method · Open · Open · 2026-08-19 · compiled 2026-10-10 · 1 min read · 1 claim · 2 X sources

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entropy · horizon · Einstein · protocol

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Dorau–Much show that the Araki–Uhlmann relative entropy of a coherent excitation on a bifurcate Killing horizon equals the energy flux across the horizon; identified with area variation, this recovers the semiclassical Einstein equations. Spradlin’s question is whether that relative entropy can be a later projection of a recoverability / response structure that is logically prior to both entropy and geometry.

This lines up interestingly with the Dorau–Much relative-entropy result. In my framework the recoverability structure exists before entropy and geometry. Curious whether the horizon relative entropy can be derived as a later projection of that pre-geometric layer.

@aaronspradlin, 19 Aug 2026 — reply on Sabine Hossenfelder’s gravity-origin thread

He asked Grok to sketch the most plausible concrete projection path and to name which existing harness sits closest: response maps, Codazzi susceptibility, W-state holonomy, or L3/L4 rank lifts. His own follow-up frames the path as “a short, executable numerical protocol whose success or failure will tell us whether the pre-geometric recoverability layer already knows about the modular relative entropy.”

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Projection from UQCF-GEM recoverability onto Dorau–Much modular relative entropy is a protocol, not a derivation. Failure is an allowed scientific outcome.

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Original posts this article was compiled from. The notebook copy is editorial; the status URL is the source.

2026-08-19

Dorau–Much relative entropy as a later projection

In the notebook · Open original post
2026-08-19

Dorau–Much as a later projection of recoverability

In the notebook · Open original post

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